Mathematical modelling of galaxies in MOND (Modified Newtonian Dynamics)
Astrophysics and Astronomy
Final Report Abstract
Motivation and background of the project is the ”missing mass problem” for spiral galaxies: The hydrogen atoms in the interstellar medium (ISM) move much faster around the galactic center than they should in the gravitational field generated by the observed matter. The analogous problem is observed in other astrophysical objects such as clusters of galaxies. Conceivable resolutions: (i) While keeping to the basis of the modeling (Newtonian mechanics, normal matter), the modeling is improved so that the discrepancy between predictions of the model and observations is reduced. Principal possibilities for this are the analysis of qualitatively new phenomena which follow from the classical model and affect the “missing mass problem”, or a detailed modeling of the components of a galaxy (stars in the central bulge and in the galactic disk, ISM). (ii) Each galaxy sits in a halo of dark matter which interacts with normal matter essentially only via gravity. (iii) The laws of gravity are modified in such a way that very weak Newtonian forces are strongly enhanced. MOND is such a modification. It can be implemented by suitably modifying the Poisson equation for the gravitational potential. The initial topic of the project was the mathematical analysis of a model modified in the sense of (iii), a nonlinear system of partial differential equations which couples the collisionless Boltzmann equation and the MONDian field equation. Introducing a suitable solution concept it was shown that suitable initial data launch global-in-time solutions to the corresponding initial value problem. Moreover, it was shown that the system has stable, stationary solutions which in principle can describe galaxies in equilibrium. In the course of the project the idea arose to improve the modeling of spiral galaxies in the sense of (i). A model of the Milky Way with a fixed central bulge and fixed galactic disk, but with a dynamic ISM was developed. The model fits the observed rotational velocity of the ISM very well, the discrepancy in the mass density between the model and observations corresponds to the Bosma effect, and the spiral structure as well as the velocity dispersion in the ISM can be explained as a consequence of certain instabilities. In parallel, a mathematical theory was developed which shows how equilibrium solutions of the Newtonian model upon perturbation start to pulse in a time-periodic way. This challenges the assumption that galaxies are in some stationary equilibrium, which usually forms the basis for investigations of the “missing mass problem”.
Publications
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On the Existence of Linearly Oscillating Galaxies. Archive for Rational Mechanics and Analysis, 243(2), 611-696.
Hadžić, Mahir; Rein, Gerhard & Straub, Christopher
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A self-consistent model for the Milky Way—Do we need Dark Matter? Poster presentation at the conference “From Stars to Galaxies II”, Gothenburg, June 20–24, 2022
Frenkler, J.
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How the spirals in the Milky Way’s ISM form.
Frenkler, J.
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Self-consistent models for Spiral Galaxies—A new chapter in the discussion about Dark Matter. Presentation at the workshop ”Mathematical Perspectives of Gravitation beyond the Vacuum Regime”, ESI Vienna, February 14–18, 2022,
Frenkler, J.
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Dynamics of Globular Clusters and Spiral Galaxies. Doctoral thesis, University of Bayreuth 2023
Frenkler, J.
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A Birman–Schwinger Principle in General Relativity: Linearly Stable Shells of Collisionless Matter Surrounding a Black Hole. Archive for Rational Mechanics and Analysis, 249(5).
Günther, Sebastian; Rein, Gerhard & Straub, Christopher
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Damping Versus Oscillations for a Gravitational Vlasov–Poisson System. Archive for Rational Mechanics and Analysis, 249(4).
Hadžić, M.; Rein, G.; Schrecker, M. & Straub, C.
